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In this paper, we analyze a full rate cooperative communication system using amplify-and-forward (AF) two-path relaying scheme with inter-relay interference cancellation at the relay. By treating AF two-path relaying as an equivalent MIMO system, we derive the pairwise error probability (PEP) of this system. Given one source node, two half duplex relay nodes, and one destination node, all equipped with single antenna, our theoretical analysis and simulation results show that diversity order of 2 can be achieved by this system. Furthermore, with inter-relay interference cancellation, degradation in performance can also be significantly reduced when inter-relay channel gain increases. Our analysis also shows that diversity order of the system will not be affected by the magnitude of this inter-relay channel gain.